Equilibrium ring concentrations and the statistical conformations of polymer chains: Part 9. Sodium metaphosphates in Graham's salt

Abstract

The molar cyclization equilibrium constants K x for oligomeric metaphosphates (NaPO 3) x in high molecular weight sodium phosphate melts at 1000K are calculated using a rotational isomeric state model to describe the statistical conformations of the corresponding open chain molecules. The model is based on a previously published analysis of the molecular structure of the polyphosphate chain. Each skeletal bond is assigned to one of three rotational states in trans ( ø=0°) and gauche ( ø=±120°) positions, and the interdependence of adjacent pairs of bond rotational states is taken into account by assuming that only Coulombic interactions between charged non-bonded atoms of the chain separated by eight or fewer chemical bonds need to be considered. The probabilities that polyphosphate chains (OPO 2) x (with x=3−10) will intramolecularly cyclize are calculated by computing the statistically weighted fraction of the 3 2 x−3 conformations defined by the rotational isomeric state model that have their termini in close proximity for ring formation. Molar cyclization equilibrium constants calculated by this direct computational method are compared with experimental values deduced from data of Thilo and Schülke, as well as with values calculated assuming that the polyphosphate chains obey Gaussian statistics.